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Abstract

Mass sensing based on mechanical oscillation frequency shift in micro/nano scale mechanical oscillators is a well-known and widely used technique. Piezo-electric, electronic excitation/detection and free-space optical detection are the most common techniques used for monitoring the minute frequency shifts induced by added mass. The advent of optomechanical oscillator (OMO), enabled by strong interaction between circulating optical power and mechanical deformation in high quality factor optical microresonators, has created new possibilities for excitation and interrogation of micro/nanomechanical resonators. In particular, radiation pressure driven optomechanical oscillators (OMOs) are excellent candidates for mass detection/measurement due to their simplicity, sensitivity and all-optical operation. In an OMO, a high quality factor optical mode simultaneously serves as an efficient actuator and a sensitive probe for precise monitoring of the mechanical eigen-frequencies of the cavity structure. Here, we show the narrow linewidth of optomechanical oscillation combined with harmonic optical modulation generated by nonlinear optical transfer function, can result in sub-pg mass sensitivity in large silica microtoroid OMOs. Moreover by carefully studying the impact of mechanical mode selection, device dimensions, mass position and noise mechanisms we explore the performance limits of OMO both as a mass detector and a high resolution mass measurement system. Our analysis shows that femtogram level resolution is within reach even with relatively large OMOs.

Figures (7)

(a) Experimental arrangement used for mass measurement using microtoroid optomechanical oscillator. (b) SEM image of one of the silica microtoroids used in this study. D = 131 µm, Dp = 5.2 µm and d = 7.8 µm. Inset: a polyethylene microbead landed on the toroidal region of the resonator. (c) Schematic diagram showing the cross–section of a microtoroid, mechanical deformation of the silica membrane (associated with the 3rd mechanical mode), and the trajectory of the circulating WG optical mode (red line).

(a) Measured RF spectrum (RBW = 30 Hz) of the OMO optical output power in the absence of the microbeads. For this OMO D = 131 µm, Dp = 5.2 µm and d = 7.8 µm and fOMO = 8.505 MHz. Here: Q0 = 6.8 × 107, Qtot = 6.72 × 106,(Qtot is the loaded optical-Q), Qmech = 1300, Pth = 553.7µW, Pin = 2.4Pth and ΔλN = 0.56 (ΔλN = Δλ/δλ, where δλ = λres/Qtot). (b) Measured RF spectrum of the OMO in the vicinity of the fundamental frequency as microbeads are added sequentially (2 through 5). (c) Images of the distribution of microbeads on the microtoroid OMO. (d) SEM image of the microtoroid OMO and the microbeads distributed on it (the distribution corresponds to c-5). (e) FEM modeling of the mechanical deformation of the corresponding mechanical mode; the contours show the total displacements. (f) Measured RF spectrum (RBW = 30 Hz) of the OMO in the vicinity of the fifth harmonic frequency as microbeads are added sequentially (1 through 5). (g) Measured frequency shift of the fundamental oscillation ΔfOMO and its 5th harmonic Δ(5fOMO) plotted against the loaded mass. The dashed red line depicts the calculated results using numerical modeling. The inset is a close-up view for Δm< 5 pg.

(a) FEM simulation of mechanical modes of a silica microtoroid. (a) Deformation of four eigen mechanical modes of a silica microtoroid with a pillar diameter Dp = 11.2 µm major diameter D = 133 µm, and minor diameter d = 7.4 µm. f0 is the eigen frequency of the corresponding mode. (b) η plotted against radial position of mass (θ = 0) for the four modes shown in part (a) using the FEM and Energy method. Compared to other modes, the η for the first mode is so small that appears as a straight line on the x-axis.

(a) Δmmin plotted against normalized detuning ΔνN for the fifth harmonic (n = 5) of the mechanical modes of the microtoroid in Fig. 2 (D = 131 µm, DP = 5.2 µm). The mass is located at the position of maximum sensitivity (ηmax = ηi(rm,θm)) for each mode. Here Q0 = 6.8 × 107, Qmech = 1300, Qtot/Q0 = 0.1 and Pin = 2 Pth. We have assumed RIN<90dB, δ(Δν0) is 500 Hz and ignored δ(Qtot/Q0) and δfI. (b) Δmmin plotted against the order of harmonic frequency used for the measurement (n) for two cases: δfI = 0 dashed lines) and δfI = 30 Hz (solid lines). The insets show the membrane deformation for the 2nd and 4th modes. The mass is located at the position of maximum sensitivity (ηmax = ηi(rm,θm)) for each mode shown as red zones in the insets. ΔλN is fixed at 0.28 that is the optimal detuning according to part-a. Other parameters are the same as the ones in part-a. (c) Δmmin plotted against the D/Dp based on the fifth harmonic shift, for D = 103 µm (dashed lines) and 133 µm (solid lines). Here all parameters are chosen according to the actual experiment. ΔλN = 0.56, Q0 = 6.8 × 107, Qmech~1400, and Pin~2 Pth. Qtot/Q0 = 0.1. Uncertainty of Qtot/Q0 and detuning δ (Δλ) are 1% and 400 KHz, respectively. Pin = 2Pth, δfI = 30 Hz.